{"ID":2876041,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.01679","arxiv_id":"2509.01679","title":"Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks","abstract":"Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the \"vanilla\" DeepONet is valued for its simplicity and efficiency, while the modified DeepONet achieves higher accuracy at the cost of increased training time. In this work, we propose a series of Transformer-inspired DeepONet variants that introduce bidirectional cross-conditioning between the branch and trunk networks in DeepONet. Query-point information is injected into the branch network and input-function information into the trunk network, enabling dynamic dependencies while preserving the simplicity and efficiency of the \"vanilla\" DeepONet in a non-intrusive manner. Experiments on four PDE benchmarks -- advection, diffusion-reaction, Burgers', and Korteweg-de Vries equations -- show that for each case, there exists a variant that matches or surpasses the accuracy of the modified DeepONet while offering improved training efficiency. Moreover, the best-performing variant for each equation aligns naturally with the equation's underlying characteristics, suggesting that the effectiveness of cross-conditioning depends on the characteristics of the equation and its underlying physics. To ensure robustness, we validate the effectiveness of our variants through a range of rigorous statistical analyses, among them the Wilcoxon Two One-Sided Test, Glass's Delta, and Spearman's rank correlation.","short_abstract":"Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the \"vanilla\" DeepONet is valued for its simplicity and efficiency, while the modified DeepONet achieves higher...","url_abs":"https://arxiv.org/abs/2509.01679","url_pdf":"https://arxiv.org/pdf/2509.01679v1","authors":"[\"Zhi-Feng Wei\",\"Wenqian Chen\",\"Panos Stinis\"]","published":"2025-09-01T18:01:23Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.NA\",\"stat.ML\"]","methods":"[\"Diffusion Model\",\"Transformer\"]","has_code":false}